{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:09:32Z","timestamp":1760148572696,"version":"build-2065373602"},"reference-count":13,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2023,5,19]],"date-time":"2023-05-19T00:00:00Z","timestamp":1684454400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003827","name":"National Research, Development and Innovation Office","doi-asserted-by":"publisher","award":["SNN 129364"],"award-info":[{"award-number":["SNN 129364"]}],"id":[{"id":"10.13039\/501100003827","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this research paper, we study 3-uniform hypergraphs H=(X,E) with circular symmetry. Two parameters are considered: the largest size \u03b1(H) of a set S\u2282X not containing any edge E\u2208E, and the maximum number \u03c7\u00af(H) of colors in a vertex coloring of H such that each E\u2208E contains two vertices of the same color. The problem considered here is to characterize those H in which the equality \u03c7\u00af(H\u2032)=\u03b1(H\u2032) holds for every induced subhypergraph H\u2032=(X\u2032,E\u2032) of H. A well-known objection against \u03c7\u00af(H\u2032)=\u03b1(H\u2032) is where \u2229E\u2208E\u2032E=1, termed \u201cmonostar\u201d. Steps toward a solution to this approach is to investigate the properties of monostar-free structures. All such H are completely identified up to 16 vertices, with the aid of a computer. Most of them can be shown to satisfy \u03c7\u00af(H)=\u03b1(H), and the few exceptions contain one or both of two specific induced subhypergraphs H5\u2941, H6\u2941 on five and six vertices, respectively, both with \u03c7\u00af=2 and \u03b1=3. Furthermore, a general conjecture is raised for hypergraphs of prime orders.<\/jats:p>","DOI":"10.3390\/sym15051114","type":"journal-article","created":{"date-parts":[[2023,5,19]],"date-time":"2023-05-19T09:23:10Z","timestamp":1684488190000},"page":"1114","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Minimal Non-C-Perfect Hypergraphs with Circular Symmetry"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0009-0007-4268-8340","authenticated-orcid":false,"given":"P\u00e9ter Bence","family":"Czaun","sequence":"first","affiliation":[{"name":"Faculty of Information Technology, University of Pannonia, Egyetem Street 10, 8200 Veszpr\u00e9m, Hungary"}]},{"given":"P\u00e1l","family":"Pusztai","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, Sz\u00e9chenyi Istv\u00e1n University, Egyetem Square 1, 9026 Gy\u0151r, Hungary"}]},{"given":"Levente","family":"Seb\u0151k","sequence":"additional","affiliation":[{"name":"Faculty of Information Technology, University of Pannonia, Egyetem Street 10, 8200 Veszpr\u00e9m, Hungary"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3235-9221","authenticated-orcid":false,"given":"Zsolt","family":"Tuza","sequence":"additional","affiliation":[{"name":"Faculty of Information Technology, University of Pannonia, Egyetem Street 10, 8200 Veszpr\u00e9m, Hungary"},{"name":"Alfr\u00e9d R\u00e9nyi Institute of Mathematics, Re\u00e1ltanoda Street 13\u201315, 1053 Budapest, Hungary"}]}],"member":"1968","published-online":{"date-parts":[[2023,5,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Beineke, L.W., and Wilson, R.J. 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Comb."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"484","DOI":"10.3390\/math9050484","article-title":"Hypercycle systems of 5-cycles in complete 3-uniform hypergraphs","volume":"9","author":"Keszler","year":"2021","journal-title":"Mathematics"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/15\/5\/1114\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T19:38:15Z","timestamp":1760125095000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/15\/5\/1114"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,5,19]]},"references-count":13,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2023,5]]}},"alternative-id":["sym15051114"],"URL":"https:\/\/doi.org\/10.3390\/sym15051114","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2023,5,19]]}}}